Because of the stochastic nature of self-amplified spontaneous emission (SASE), it is crucial to measure for single pulses the spectral characteristics of ultrashort pulses from the vacuum ultraviolet free electron laser (FLASH) at DESY, Germany. To meet this particular challenge, we have employed both photon and photoelectron spectroscopy. Each FEL pulse is composed of an intense and spectrally complex fundamental, centered at a photon energy of about 38.5 eV, with a bandwidth of 0.5% accompanied by higher harmonics, each carrying an intensity of typically 0.3 to 0.6% of that of the fundamental. The correlation between the harmonics and the fundamental is in remarkable agreement with a simple statistical model of SASE FEL radiation.